There is a difference between forgiving and over-looking a transgression. As some have posted already, over-looking, dismissing, letting go, whatever you want to call it, is for our own peace of mind. It is not healthy to hold on to negative feelings because it only hurts us in the end.
A circuit overseer asked the question to the congregation, "How many have been hurt and were able to 'forgive and forget' the transgression of their brother or sister?" He asked that hands be raised. When more than half the congregation raised their hands, he laughed and said, "You see, you haven't forgotten." Forgiving someone when they have never asked for our forgiveness is ridiculous. The scriptures say that God forgives freely so we should also.
The issue is not that God forgives, it is when. God forgives us when we ask for his forgiveness. If we are asked to forgive others, when they demonstrate no remorse, is asking us to do something that God would never do. If God forgave indiscriminately, then there would not be any need for judgement or concern about accountability. The wrong application of this principle has been a burden to many sincere Christians and I'm sure has led many away from an organization that makes excuses for it's cruelty and indiscretions.
If a person has hurt me and then sincerely asks for my forgiveness, it would be ridiculous for me not to. They have made the effort to repair the relationship and I would love them even more for thinking enough of me to care. If they don't feel compelled to apologize, then I would just try to dismiss it because my emotional health or spirituality could be damaged. It's not that easy to do, especially when you have people that distort the scriptures to accomodate their fleshly perspectives.
I like thinking of why I ask for forgiveness when I was wrong about something. It reminds me of the love and friendship that I have for those I care about. Imperfection means I am going to grow old and die. It is not a convenient excuse that I can pull out whenever I have wronged somebody. Excuses expose the heart. "Love covers a multitude of sins", doesn't mean we can just walk all over people and test their love for us.
